Today, the FMS calculates a flight plan to be followed which reaches particular points of the flight plan at precise times, in the most effective possible manner and, for example, in an economical manner. The flight plan to be followed is calculated so as to comply with a required time of arrival at a constrained point (that is to say so that the aircraft reaches the constrained point at the required time of arrival), which time is commonly referred to by the acronym RTA for “Required Time at Arrival”.
Currently, the FMS of an aircraft regularly verifies whether the aircraft is following the flight plan to be followed. When at a current position on the lateral trajectory, the aircraft strays from the flight plan to be followed (that is to say strays from the predetermined tolerances in the vertical flight plane or in the speed profile with respect to the respective trajectories in these planes), the FMS calculates a new flight plan, called the homing flight plan, assumed to have to be followed by the aircraft that has left the flight plan to be followed, homing in on the flight plan to be followed. The homing flight plan includes an estimated lateral trajectory, an estimated vertical trajectory and an estimated speed profile. Homing in on the flight plan to be followed is understood to mean that the estimated vertical trajectory, the estimated lateral trajectory and the estimated speed profile approach respectively the vertical and lateral trajectories to be followed and the speed profile of the flight plan to be followed until they have been homed in on. The homing flight plan is calculated by prediction on the basis of a current position of the aircraft. When the aircraft is assumed to follow a predetermined lateral trajectory, the homing flight plan includes an estimated speed profile, an estimated vertical trajectory and the lateral trajectory. The speed profile to be followed is the horizontal component of the speed to be followed. When the estimated speed profile links up with the speed profile to be followed, it is therefore the horizontal component of the estimated speed which approaches the speed profile. In aeronautics, the quantities used to define the speed profile are the CAS (Calibrated Air Speed, corresponding to the speed read on the onboard instruments) and the MACH (corresponding to the Mach number). The “horizontal component of the speed to be followed” (hereinafter called the “speed profile to be followed”) therefore corresponds to one of these quantities. Hereinafter, the component of the speed of the aeroplane in the horizontal plane, expressed in the units of these quantities CAS or MACH, will be called the “horizontal speed”. The homing flight plan is obtained by integrating the state vector of the aircraft, from a current position P of the aircraft, along the forthcoming lateral trajectory (that is to say at constant lateral trajectory) as a function of a homing guidance directive.
A prediction calculation performed so as to home in on the flight plan to be followed corresponds to integrating the state of the aeroplane (according to equation 1 below) on the basis of a guidance directive, called the homing guidance directive, adapted so that the aircraft homes in on the flight plan to be followed. Indeed, the state X of the aeroplane is conventionally related to the guidance directive U by the following equation:dX/dt=f(X,U)  (1)where dX/dt is the derivative of the state of the aircraft with respect to time.
The state of the aircraft is a vector conventionally including the following coordinates: the position of the aircraft in the horizontal plane, its altitude, its ground speed (or speed of the aircraft with respect to the ground), its vertical speed, the air speed (or speed in the air mass), the fuel, the time. The ground speed is equal to the air speed to which is added the wind (the whole in vector form, projected onto the horizontal plane). The speed of the aircraft is the vector composed of the vertical speed and of the ground speed of the aircraft, in vector form.
Represented in FIGS. 1a and respectively 1b on a descent and approach phase between a departure point PD and an arrival point PA situated at a distance da from the departure, are examples of curves of variation of the altitude and respectively of the horizontal speed of an aircraft as a function of the distance traveled along the lateral trajectory. The curves represented solid in FIGS. 1a, respectively 1b, represent the vertical trajectory to be followed PH and the speed profile to be followed PV. The curves represented dashed in FIGS. 1a and respectively 1b represent an estimated vertical trajectory PHE and respectively an estimated speed profile PVE. In FIGS. 1a and 1b, it is noted that at the current point P situated a distance dP from the start of the descent phase on the lateral trajectory, the aircraft exhibits a current horizontal speed V and current altitude H. In FIG. 1a, the current altitude is greater than the altitude h defined by the vertical trajectory to be followed PH at the current point. The altitude difference DH is greater, in absolute value, than a predetermined altitude tolerance TH, not represented.
The state of the aircraft is integrated as homing guidance directive function including between the current point P and a linkup point in terms of horizontal speed RV situated a distance dv from departure, a linkup guidance directive. More particularly between the current point P and a first point P1 situated a distance d1 from departure, a linkup guidance directive of the type “acceleration under slowed thrust” chosen so that the slope FPA (not represented) formed between the aircraft and the ground is greater than that which is defined by the vertical trajectory to be followed so as to allow the aircraft to approach the vertical trajectory to be followed. Between the current point and the point P1, the estimated horizontal speed of the aircraft increases (and is greater than the horizontal speed of the speed profile to be followed). Once the estimated vertical trajectory is sufficiently close to the vertical trajectory to be followed, here at the point P1, the FMS integrates the state of the aircraft as a function of a linkup guidance directive of the slowdown type, so that the estimated vertical trajectory links up with the trajectory to be followed (at the altitude linkup point RH situated a distance dh from departure) and the estimated speed links up with the speed to be followed (at the speed linkup point RV). For a conventional aircraft where the vector U of guidance directives includes two components, namely the attitude of the aeroplane (or slope FPA) and the thrust of the engines, it is possible to use the attitude to accelerate (increase the thrust) or slow down (decrease the attitude). The estimated vertical trajectory PHE includes an estimated vertical linkup trajectory PHEInk extending between the current point and the altitude linkup point RH, followed by an estimated vertical follow trajectory PHEfollow coinciding, to within a tolerance, with the vertical trajectory to be followed. The estimated speed profile PVE includes an estimated linkup profile PVEInk extending between the current point and the speed linkup point RV, followed by an estimated follow speed profile PVE follow coinciding, to within a tolerance, with the speed profile to be followed.
As soon as the estimated vertical speed profile and the estimated vertical trajectory have linked up with the speed profile to be followed and respectively the vertical trajectory to be followed, that is to say between the speed linkup point RV and the arrival point PA situated at a distance da from departure, the FMS integrates the state of the aircraft along the flight plan to be followed. Everything happens as if the FMS integrated the state of the aircraft according to a guidance directive called the follow guidance directive adapted so that the estimated speed profile and the estimated vertical trajectory are equal to within the respective tolerances, to the speed profile to be followed and to the vertical trajectory to be followed. Stated otherwise, after the respective homing points, the estimated profiles and trajectories follow respectively the profiles and trajectories to be followed. The homing guidance directive therefore includes a linkup guidance directive followed by a follow guidance directive.
The FMS calculates the estimated time of arrival at the constrained point, namely the time at which the FMS forecasts that the aircraft will reach the constrained point. The estimated time of arrival is commonly referred to by the acronym ETA. It is conventionally calculated by integrating the state vector X of the aircraft as a function of the homing guidance directive over the forthcoming lateral trajectory. If the estimated time of arrival strays from a predetermined tolerance, called the absolute tolerance T, with respect to the required time of arrival RTA, a new cycle of calculations takes place, leading the FMS to redefine the flight plan to be followed by taking account of the time constraint to be complied with and a homing flight plan when the aircraft strays from the flight plan to be followed. The objective is to cause the estimated time of arrival calculated on the basis of the guidance directive to converge on the required time of arrival. The tolerance in relation to the required time of arrival is generally modelled in the form of a funnel, that is to say it is increasingly narrow as the aircraft approaches the constraint point. For the calculation of the homing flight plan in the case where the aircraft follows a predetermined lateral trajectory, the FMS has only two degrees of freedom, namely the thrust and the attitude, to define the homing guidance directives ensuring the homing of the flight plan to be followed. Thus the guidance directive acts on the speed of the aircraft.
The time of passage at a determined point (or time profile) being a consequence of the speed profile, each time that the aircraft leaves the vertical trajectory to be followed, the guidance directive determined by the guidance module acting on the horizontal speed of the aircraft gives rise to a failure to adhere to the time constraint. A divergent infinite loop then occurs in the iteration process described previously, generally leading to non-compliance with the time constraint but possibly also having a negative impact on the adherence to the altitude and speed profiles to be followed.
Operationally, the pilot notes that immediately after the calculation of a flight plan to be followed the aircraft complies with the time constraint but that after the determination of a guidance directive bringing the aircraft back onto the flight plan to be followed, the aeroplane begins to deviate temporally from the time constraint. After a certain time, the estimated time of arrival differs from the required time of arrival and a new calculation of the speed profile and of the vertical trajectory to be followed takes place so as to attempt to comply with this time constraint, entailing the calculation of a new guidance directive, differing from the previous one. From the guidance point of view, this brings about jumps, engine jerks if the guidance directives for ensuring linkup change from one loop to another. The aeroplane guidance not succeeding in stabilizing on a guidance directive which complies with the constraint, the flight management system is not reliable. The crew tend to terminate their manoeuvre manually. Moreover, the changes of guidance directive are uncomfortable for the passengers. The instability of the status of the time constraint (which passes from the ‘successful’ state to the missed state in each iteration) is also counter-productive in relation to the air traffic control authorities which are generally the originators of the time constraint. They note that the aeroplane no longer complies with a time constraint and they may therefore make a needless, or indeed counter-productive decision to manage the guidance of the aircraft.